How much data do you want for your progress? Quantitative History and the Study of Social Problems

Nathan Alexander, PhD

Howard University

Framing our time.

  • A bit about me.

  • Our lab, the Quantitative Histories Workshop.

  • How much data do you want for your progress?

A bit about my ancestors, my journey, teachers, and students.

A stolen people on stolen land.

My ancestors come from the coast of the Carolinas (NC and SC), where enslaved Africans entered what is now known as the United States. I was born in Charlotte, NC. Meaning that, over time, like many other Black families, there was little movement beyond the South.

The Carolinas, from the Equal Justice Initiative (2026)

My family has very few historical records of our ancestors.

My maternal ancestors circa 1900

In 1971, Charlotte, NC, became a national model for school desegregation through court-ordered busing following the landmark Swann v. Charlotte-Mecklenburg Board of Education Supreme Court ruling. In 1989, at the age of 5, I would become part of this desegregation plan.

Busing as a result of Swann v. Charlotte-Mecklenburg Board of Education

I was raised in a public housing project in South Charlotte, known as Boulevard Homes in the 90s. These projects were just one exit, a literal two-minute drive, from the Charlotte Airport. This meant that we were in a food and transportation desert next to a busy roadway, Billy Graham Parkway, separated only by a single line of trees.

Boulevard Homes Public Housing Project, Charlotte, NC

Despite our economic conditions, my parents supported our learning and well-being.

My 5th birthday party with my sisters and cousins.

By mere luck, I would be bused to Selwyn Elementary, the #1 elementary school in Charlotte at the time. For context, the surrounding median home value as of Feb. 2026 is $2,524,5001.

Selwyn Elementary School

The mathematics of opportunity.

As a result of busing, I would have access to educational resources that my first cousins, who lived in the housing project across the street, known as Little Rock in the 90s, would not be able to access. Their bus took them to a different school on the other side of Charlotte.

I recently published a paper on this issue in the Journal of Negro Education.

  • Alexander, N. N. (2024). Measuring School Desegregation: A Critical Quantitative Replication. The Journal of Negro Education, 93(3), 318-331.

In this paper, I discuss a mathematical model used to measure segregation, known as the Index of Dissimilarity, and its relationship to the 70th Anniversary of the 1954 Brown v. Board of Education of Topeka Supreme Court decision. More on this later…

\[ D = \frac{1}{2} \sum_{i=1}^n \left| \frac{b_i}{B} - \frac{w_i}{W} \right| \]

For the love of mathematics.

My first club at Alexander Graham Middle School

I would then spend a summer in Boone, NC with the Summer Ventures Program. It was here that I decided I wanted to be an architect, after spending most of my time building housing structures with balsawood.

Summer Ventures Program

The transition to my undergraduate studies.

Phillips Hall, UNC Department of Mathematics

@UNC - Double major in mathematics and sociology.

I was the only Black math major in the department.

I would fall in love with coding in my statistics courses in sociology.

UNC Math Department Newsletter

My 1st math course at UNC

MATH 89H - First Year Honors Seminar – Fractals. Taught by Sue Goodman, Topologist.

We spent the first-half of the term making connections to the real world; most literally, going outside to observe tree bark, patterns in the grass, reading books (e.g., The Labryinth), and writing “fractal” poems.

Fractal Geometry

During the second-half of the term, we would formalize our observations. Starting with the Mandelbrot set and extended it to similar forms, such as the Julia set. A Julia set is a bunch of fractals that are similar to the Mandelbrot Set. It is a set defined given a rational function, \(J(f)\), such that all nearby values behave similarly when the function is repeatedly iterated.

A Julia Set

My 2nd math course at UNC

Calculus of Functions of Several Variables

My second math course was in stark contrast to what I had imaged the rest of my mathematical experiences would be in college. I would spend nearly every day after class with Dr. Petersen, building my first honest relationship with a professor.

Karl Petersen, Ergodic theory

My job as a grader and teaching assistant

UNC Math Help Center

Differential Equations and Linear Algebra for Applications

James Damon, Singularity theory

Noberto Kerzman (1943-2019), Complex analysis

Introduction to Real Analysis

Dr. Assani, a Beninese mathematician, joined the UNC mathematics department in 1988 but, for racist reasons, was turned down for tenure. He appealed through the courts, won his case and gained tenure in 1995, and was promoted to full professor one year later. In doing so he became the first Black tenured associate mathematics professor and the first Black full mathematics professor at UNC, as well as the only mathematician there to be promoted from associate to full so quickly (Mathematicians of the African Diaspora, 2014)

Idris Assani, Ergodic theory

Study Abroad at the National University of Singapore

I was selected as part of a first group of students to travel to the National University of Singapore as part of a new exchange program. Given the newness of the program, we would travel early to meet students in Singapore, whose families would serve as our hosts over the holiday break, and they would then leave for UNC at the start of the spring.

NUS

My favorite course at the National University of Singapore

In The Horror of the Other, a humanities and social science elective, we examined the concept of othering. I would write my first interdisciplinary mathematical analysis of social science concepts using the ideas of equivalence relations, sameness, and difference.

Chitra Sankaran, NUS, Humanities and Social Sciences

The Others

Junior Year back @ UNC

At Carolina (UNC), the Department of Mathematics is next door to the School of Education. When I returned my junior year, I would meet Dr. Carol Malloy, a famous mathematics educator and faculty member in the School of Education.

Carol Malloy, 1944-2015, UNC School of Education

Lead Math Tutor at UNC’s Upward Bound Program

As a result of meeting Dr. Malloy, I would be asked to become the lead tutor for UNC’s Upward Bound program. This would be on top of my job as a TA and grader in the mathematics department. I would tutor undergraduates during the week and teach mathematics to high school students on Saturday mornings.

UNC Upward Bound Program

Master of Arts in Teaching @ New York University

I would accept a scholarship to NYU to learn how to teach mathematics. While in New York, I would study under Dr. Karen King, who taught me theories of education and the pedagogy of mathematics. Dr. King would challenge me to create culturally relevant math lessons.

Karen King, 1971-2019, MAT advisor

Student Teaching

Pre-service teachers are required to complete about 200 hours of student teaching in a local high school. I was placed at a school for recent Chinese immigrants in the Lower East Side (LES) of New York at the LES Community School. Here, I created my first ethnomathematics unit plan.

Camping trip with students from Lower East Side Community School, 2008

Teacher of Record

My first teaching experience as the teacher of record would be in Bedstudy, Brooklyn, NY at a middle school for Boys. I would move from Brooklyn to Harlem to teach at the Harlem Children’s Zone. I would be tapped by the COO, George Khaldun, to support org-wide statistical analysis with external, mostly white, business consultants. Given their lack of contextual knowledge, I became interested in getting a PhD to combat their deficit narratives of the youth and families.

TRUCE @ Harlem Children’s Zone

PhD program in Mathematics and Education @ Columbia University

I would go on to study in the Program in Mathematics at Teachers College, Columbia University. The first program of its kind in the country. In this program, 75 credit hours over 5 years, we take PhD courses and qualifying exams in mathematics (I completed exam requirements in Topology/Geometry, Statistics & Probability Theory, and Analysis) and advanced theory courses in mathematical education. This allows us to work in both departments of mathematics and schools of education.

Teachers College, Program in Mathematics

Doctoral work as a Gradaute Research Assistant

I studied under Dr. Erica Walker, who studies the histories and social networks of Black mathematicians. As her graduate assistant, I would begin my initial foray into archival research as she completed her book, Beyond Banneker.

Erica Walker, my PhD advisor

Beyond Banneker by Erica Walker

Quantitative Histories Workshop

curriculum & software development collective

and

research lab

Research Problem

Increasingly complex problems require complex tools.

Computational tools support interdisciplinary thinking.

Research Problem

Increasingly complex problems require complex tools.

Computational tools support interdisciplinary thinking.

Research Problem

Increasingly complex problems require complex tools.

Sub-disciplinary tools require interdisciplinary thinking.

How might information theories inform interdisciplinary curriculum and software development?

Information theory

Information theory is a branch of applied mathematics and computer science that deals with the quantification, storage, transmission, and manipulation of information. We take an abstract approach to our study of information.

  • Information theory seeks to measure the amount of information contained in a message or signal and how efficiently it can be transmitted or stored.

  • In this way, our projects define information using a curricular perspective.

  • Namely, how might faculty and educators leverage computation and quantification to transmit information efficiently while maintaining the roots of complex theories and concepts?